[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274380-105":59,"doc-detail-274380-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","shsat-math-problems","SHSAT Math Problems","","A collection of SHSAT-style multiple-choice mathematics problems covering geometry, number and algebra, coordinate geometry, and word problems. Topics include triangle and angle relationships, circles and tangent properties, polygon interior angles, areas and perimeters of composite shapes, and solving equations or expressions. Additional questions test inequalities, ratios, and algebraic transformations, often requiring selection of the single correct value from several options.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/shsat-math-problems/274380/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/shsat-math-problems/274380.png","ImageObject",300,407,{"name":92,"@type":93},"Aria Callaghan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",36,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What kinds of geometry topics are included in these SHSAT math problems?","Question",{"text":113,"@type":114},"The set covers angles in triangles, squares, and regular polygons, as well as circle theorems involving diameters, tangents, and central-angle relationships.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Do the problems include questions about area and perimeter?",{"text":118,"@type":114},"Yes. There are multiple questions asking for areas of triangles and trapezoids and for perimeters or lengths in composite or shaded figures.",{"name":120,"@type":111,"acceptedAnswer":121},"What algebra skills do these problems test?",{"text":122,"@type":114},"They test solving equations for variables, simplifying expressions, working with inequalities, and finding ratios or values that satisfy given relationships.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},274380,1789476785,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144},962084926284,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","DCB is a right triangle,and pointA lies on the line segment CD.IfAC=BC=2,and BD=4,find AD.  \nF.10  \nG.2√3  \nH.2√3-2  \nJ.√3+2  \nK.None of these  \nFour lines on the plane have atmostN common points.Find N.  \nF.7  \nG.6  \nH.5  \nJ.4  \nK.3  \nEF is a diameter of a circle withcenter R.D is a point on the samecircle.If the measure of angleDRF is 42°,what is the measure ofangle DEF?  \nA.42  \nB.41°  \nC.35°  \nD.21°  \nE.  19°  \nABCD is a square,and AED is anequilateral triangle.Find themeasure of angle BEC.  \nA.160°  \nB.150°  \nC.120°  \nD.115°  \nE.110°  \nIf the area of the trapezoid is(d+b)×c,then what is a in termsof b?  \nA.2b  \nB.b  \nC.b+2  \nD.2b+2  \nE.None of these  \nThree different lines on a planedivide it into k regions,which donot overlap.The number k cannotbe  \nA.7  \nB.6  \nC.5  \nD.4  \nE.k could be any number  \nTwo congruent circles with centersat points O and C overlap eachother.Radii OD=CO=3.What isthe length of the part of the leftcircle that is contained in the rightcircle?  \nF.   4π  \nG.   3π  \nH.   2π  \nJ.     π  \nK.  0.5π  \nPABCDE is a regular pentagon.If∠CBP=20°,and EDP is a linesegment,Find the degree measureof ∠BPD.  \n##### A.  10°\n\nB.  12°  \nC.  14°  \n##### D.  16°\n\nE.  18°  \n### 93.What is the area of the triangle thatthe liney=2-x,thex-axis,and they-axis form in the first quadrant?\n\nA.  1 sq.unit  \nB.  2 sq.units  \nC.  3 sq.units  \nD.  4 sq.units  \n##### E.  6 sq.units\n\nIf the area of the rectangle ABCD  \nis 68 sq ft and the distance  \nbetween vertex Band the diagonalAC is 2ft,what is AC?  \n##### F.34 ft\n\nG.17 ft  \n### H.68 ft\n\nJ.64 ft  \nK.None of these  \nQ  \nR  \nTQ(not shown)=17cm,TR=8cm.Find the perimeter of entire shape.  \nF.  46 cm  \nG.  44 cm  \n##### H.  28 cm\n\nJ.  26 cm  \nK.  24 cm  \nWhat is the degree measure of thesmallest angle between two lines ofsymmetry of a regular octagon?  \nF.  12.5°  \nG.    20°  \nH.  22.5°  \nJ.   30°  \nK.   45°  \nT  \nThe perimeter of the square PQRTis 4.The length of QV could be:  \nA.  2  \nB.  1.7  \nC.  1.5  \nD.  1.3  \nE.  1  \nB  \nThree congruent circles with radii 2cm are tangent to each other anddivided into 4 congruent parts,asshown above.Find the distance AB.  \nA.  8√2  \nB.6√2  \nC.  6√3  \nD.4√2  \nE.  4√3  \n92.Ifx²y³z³\u003C0,which statement mustbe true?  \nF.xy>0  \nG.yz\u003C0  \nH.  xz\u003C0  \nJ.xyz\u003C0  \nK.   x\u003C0  \n66.  \nMN  \nRegular pentagon is inscribed into acircle.If O is the center of the circle,Find the degree measure of the angleMON.  \nF.  288°  \nG.  150°  \nH.  144°  \nJ.  130°  \nK.  120°  \n84.  \nBA  \nAB is tangent to circle O withradius 6.and ∠ABO=30°.Find thearea of the shaded region.  \nF.18√3-6π  \nG.    18-6π  \nH.36√3-6π  \nJ.  6√3-6π  \nK 9√3-6π  \n100.  What is the degree measure of thesmallest angle between hour andminute hands of a clock at  \n11:10 PM?  \nF.70°  \nG.75°  \nH.85°  \nJ.86°  \nK.90°  \nIn the diagram above,the diameterof the inner circle is equal to theradius of the large circle.Two circlestangent each other.What part of thelarge circle is shaded?  \nA.  \nB.  \nC.  \nD.  \nE.  \nFigure is not drawn to scale.  \nPoints C,D,and E are on thecircumference of a circle.O is thecenter of the circle,and CD=5.If∠CFD=30°,find perimeter ofDOEF.  \n#### F.  10\n\n## G.12.5+5√3\n\nH.10+√3  \nJ.  10+5√3  \nK.  20  \n64.  \nIn the diagram above,which of thefollowing could be a value ofy?  \nF.  20°  \n#### G.  30°\n\nH.  35°  \nJ.  60°  \nK.  65°  \n79.  \nb  \nFind the value of c,if a+b=9,andab=16.  \nA.  2  \nB.  4  \nC.  6  \nD.  7  \nE.  9  \n#### 87.If a circle is inscribed into a squarewith the side of 4 inches,what is thedistance between the vertex of thesquare and the point on the circleclosest to it?\n\n## A.      2\n\nB.     √2  \nC.    2√2  \n## D.2√2-1\n\nE.2√2-2  \nWhat is the degree measure of the  \nsmaller angle between the hourand minute hands of the clock at  \n5:10 PM?  \n#### F.110°\n\nG.105°  \nH.100°  \nJ.95°  \nK.90°  \nA.-2  \nB.  -1.5  \nC.  0  \nD.  1  \nE.    1.5  \n72.If/2a=3b,and 6b=5c what is theratio of a to c?  \n#### F.  5:4\n\nG.  3:5  \nH.  4:5  \nJ.  5:3  \nK.  None of these  \nIf 3a=2b,5b=3c,and 5c=4d,what is the ratio ","cbCailrkdIBXfJ46","https://ap.wps.com/l/cbCailrkdIBXfJ46","pdf",4807195,"English","# Geometry and Angles\n## Triangles, squares, and polygons\n## Circles, diameters, tangents, and shaded regions\n# Area and Perimeter\n## Trapezoids and rectangles\n## Perimeter of composite figures\n# Algebra and Equations\n## Solving for variables and expressions\n## Ratios, inequalities, and number properties\n# Coordinate Geometry and Word Problems","[{\"question\":\"What kinds of geometry topics are included in these SHSAT math problems?\",\"answer\":\"The set covers angles in triangles, squares, and regular polygons, as well as circle theorems involving diameters, tangents, and central-angle relationships.\"},{\"question\":\"Do the problems include questions about area and perimeter?\",\"answer\":\"Yes. There are multiple questions asking for areas of triangles and trapezoids and for perimeters or lengths in composite or shaded figures.\"},{\"question\":\"What algebra skills do these problems test?\",\"answer\":\"They test solving equations for variables, simplifying expressions, working with inequalities, and finding ratios or values that satisfy given relationships.\"}]","SHSAT Math Problems | PDF",18]